On a subproblem of trust region algorithms for constrained optimization |
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Authors: | Y Yuan |
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Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW, England |
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Abstract: | We study a subproblem that arises in some trust region algorithms for equality constrained optimization. It is the minimization of a general quadratic function with two special quadratic constraints. Properties of such subproblems are given. It is proved that the Hessian of the Lagrangian has at most one negative eigenvalue, and an example is presented to show that the Hessian may have a negative eigenvalue when one constraint is inactive at the solution.Research supported by a Research Fellowship of Fitzwilliam College, Cambridge, and by a research grant from the Chinese Academy of Sciences. |
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Keywords: | Subproblem constrained optimization quadratic constraints trust region algorithms |
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